Properties

Label 3024.2.ek
Level 3024
Weight 2
Character orbit ek
Rep. character \(\chi_{3024}(611,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 752
Sturm bound 1152

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Defining parameters

Level: \( N \) = \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3024.ek (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1008 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3024, [\chi])\).

Total New Old
Modular forms 2352 784 1568
Cusp forms 2256 752 1504
Eisenstein series 96 32 64

Trace form

\( 752q - 4q^{4} + 6q^{5} - 4q^{7} + O(q^{10}) \) \( 752q - 4q^{4} + 6q^{5} - 4q^{7} - 4q^{10} + 6q^{11} - 4q^{13} + 6q^{14} - 4q^{16} - 4q^{19} + 12q^{20} - 4q^{22} + 12q^{23} - 16q^{28} + 12q^{29} - 8q^{34} + 30q^{35} - 4q^{37} + 6q^{38} + 2q^{40} - 4q^{43} - 66q^{44} + 4q^{46} - 4q^{49} + 12q^{50} + 2q^{52} - 32q^{55} - 36q^{56} + 2q^{58} - 4q^{61} - 16q^{64} - 4q^{67} + 54q^{68} + 26q^{70} + 90q^{74} - 4q^{76} + 6q^{77} + 72q^{83} - 14q^{85} + 66q^{86} + 2q^{88} + 20q^{91} + 12q^{92} - 36q^{94} - 8q^{97} - 114q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3024, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database